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# Graphical Examination of Data - PowerPoint PPT Presentation

Graphical Examination of Data. 1.12.1999 Jaakko Leppänen [email protected] Sources. H. Anderson, T. Black: Multivariate Data Analysis, (5th ed., p.40-46) . Yi-tzuu Chien: Interactive Pattern Recognition, (Chapter 3.4) .

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### Graphical Examination of Data

1.12.1999

Jaakko Leppänen

[email protected]

• H. Anderson, T. Black: Multivariate Data Analysis,(5th ed., p.40-46).

• Yi-tzuu Chien: Interactive Pattern Recognition,(Chapter 3.4).

• S. Mustonen: Tilastolliset monimuuttujamenetelmät,(Chapter 1, Helsinki 1995).

• Examining one variable

• Examining the relationship between two variables

• 3D visualization

• Visualizing multidimensional data

• Histogram

• Represents the frequency of occurences within data categories

• one value (for discrete variable)

• an interval (for continuous variable)

• Stem and leaf diagram (A&B)

• Presents the same graphical information as histogram

• provides also an enumeration of the actual data values

• Scatterplot

• Relationship of two variables

Linear

Non-linear

No correlation

• Boxplot (according A&B)

• Representation of data distribution

• Shows:

• Middle 50% distribution

• Median (skewness)

• Whiskers

• Outliers

• Extreme values

• Good if there are just 3 variables

• Mustonen: “Problems will arise when we should show lots of dimensions at the same time. Spinning 3D-images or stereo image pairs give us no help with them.”

• Scatterplot with varying dots

• Scatterplot matrix

• Multivariate profiles

• Star picture

• Andrews’ Fourier transformations

• Metroglyphs (Anderson)

• Chernoff’s faces

• Two variables for x- and y-axis

• Other variables can be represented by

• dot size, square size

• height of rectangle

• width of rectangle

• color

• Also named as Draftsman’s display

• Histograms on diagonal

• Scatterplot on lower portion

• Correlations on upper portion

correlations

histograms

scatterplots

• Shows relations between each variable pair

• Does not determine common distribution exactly

• A good mean to learn new material

• Helps when finding variable transformations

• Color level represents the value

• e.g. values are mapped to gray levels 0-255

• A&B: ”The objective of the multivariate profiles is to portray the data in a manner that enables each identification of differences and similarities.”

• Line diagram

• Variables on x-axis

• Scaled (or mapped) values on y-axis

• An own diagram for each measurement (or measurement group)

• Like multivariate profile, but drawn from a point instead of x-axis

• Vectors have constant angle

• D.F. Andrews, 1972.

• Each measurement X = (X1, X2,..., Xp) is represented by the function below, where - < t < .

• If severeal measurements are put into the same diagram similar measurements are close to each other.

• The distance of curves is the Euklidean distance in p-dim space

• Variables should be ordered by importance

• Can be drawn also using polar coordinates

• Each data vector (X) is symbolically represented by a metroglyph

• Consists of a circle and set of h rays to the h variables of X.

• The lenght of the ray represents the value of variable

• Normally rays should be placed at easily visualized and remembered positions

• Can be slant in the same direction

• the better way if there is a large number of metrogyphs

• Theoretically no limit to the number of vectors

• In practice, human eye works most efficiently with no more than 3-7 rays

• Metroglyphs can be put into scatter diagram => removes 2 vectors

• H. Chernoff, 1973

• Based on the idea that people can detect and remember faces very well

• Variables determine the face features with linear transformation

• Mustonen: "Funny idea, but not used in practice."

• Originally 18 features

• Radius to corner of face OP

• Angle of OP to horizontal

• Vertical size of face OU

• Eccentricity of upper face

• Eccentricity of lower face

• Length of nose

• Vertical position of mouth

• Curvature of mouth 1/R

• Width of mouth

• Face features (cont…)

• Vertical position of eyes

• Separation of eyes

• Slant of eyes

• Eccentricity of eyes

• Size of eyes

• Position of pupils

• Vertical position of eyebrows

• Slant of eyebrows

• Size of eyebrows

• Graphical Examination eases the understanding of variable relationships

• Mustonen: "Even badly designed image is easier to understand than data matrix.”

• "A picture is worth of a thousand words”